Abstract: A theoretical method is proposed to calculate energy spectrum of spin motion of one-dimensional ferromagnetic and antiferromagnetic chains.By using a complete orthonormal set in the Hilbert space,the Hamiltonian of the spin system can be transformed into the Hermitian matrix,and the eigenvalues of the Hermitian matrix were resolved,thus the energy spectrum of the spin system can be determined.The method can easily translated into the computer program and can also be applied to other magnetic systems.